Optical fiber interferometric sensors based on [3×3] couplers have been used in many fields. A new technique is proposed to demodulate output signals of this kind of sensors. The technique recovers the signal of interest by fitting coefficients of elliptic (Lissajous) curves between each fiber pair. Different from other approaches, this technique eliminates the dependence on the idealization of [3×3] coupler, provides enhanced tolerance to the variance of photoelectric converters, and is anti-po